Asymptotic solutions of differential rotation driven by convection in rapidly rotating fluid spheres with the non-slip boundary condition

A strong Coriolis force in a rapidly rotating planet and star not only enforces two-dimensionality of fluid motion driven by thermal instabilities but also generates strong differential rotation even in the vicinity of the onset of instabilities. We derive an asymptotic solution describing convection-driven differential rotation in rotating, self-gravitating Boussinesq fluid spheres with the no-slip boundary condition, taking into account full spherical curvature and being valid for asymptotically small Ekman numbers. For the purpose of validating the asymptotic solution, the corresponding numerical analysis valid for large or small Ekman numbers is also carried out, showing a satisfactory agreement between the asymptotic and numerical solutions.